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Abstract

We propose a most economical design of the Optical Shared MemOry Supercomputer Interconnect System (OSMOSIS) all-optical, wavelength-space crossbar switch fabric. It is shown, by analysis and simulation, that the total number of on-off gates required for the proposed N × N switch fabric can scale asymptotically as N ln N if the number of input/output ports N can be factored into a product of small primes. This is of the same order of magnitude as Shannon’s lower bound for switch complexity, according to which the minimum number of two-state switches required for the construction of a N × N permutation switch is log2 (N!).

Multiplexing/demultiplexing functionalities of the 16 × 16 optical interconnect of Fig. 3. (a) At the transmitter, the 16-channel multiplexing hierarchy can be represented by a tree structure. The root tributary is composed of four wavebands of four wavelengths each. (Symbols: The four wavebands are denoted from left to right with black, red, green, and blue lines. Same color code is used for the wavelengths within each waveband). (b) At the receiver, it is possible to reduce the number of SOAs by folding the tree structure of the multiplexing hierarchy, exploiting the periodicity of the AWG transfer function. The folded tree, as it appears after a Waveband MUX/DMUX pair and an AWG Wavelength DMUX, is shown here. By placing SOAs at the arms of the DMUXs at the waveband- and wavelength-level (i.e., the branches and the leaves of the folded tree), it is possible to reduce the number of SOAs by half. In order to achieve this, the wavelength DMUX must be an AWG.

Alternative implementation of the multiplexing/demultiplexing functionalities of Fig. 4. (a) At the transmitter, hierarchical multiplexing is performed using four fibers carrying the same set of four wavelengths, instead of one fiber carrying four wavebands of four distinct wavelengths each (i.e., a total of 16 wavelengths) as in Fig. 4; (b) Receiver: The Waveband MUX/DMUX pair at the receiver of Fig. 4 is omitted here. The Waveband MUX at the receiver of Fig. 4 is substituted by a combiner. The folded tree, as it appears after a combiner and a Wavelength DMUX, is shown here. By placing SOAs at the arms of the DMUXs at the fiber- and wavelength-level (i.e., the branches and the leaves of the folded tree), it is possible to reduce the number of SOAs by half. The wavelength DMUX does not have to be AWG.

(a) Example of K multiplexing stages with n1 channels per waveband of order one (i = 1), n2 wavebands of order one per waveband of order two (i = 2), and so on. The K-th multiplexing stage can be implemented using spatial division multiplexing (SDM) of nk optical fibers, in order to allow wavelength reuse and hence, reduce the total number of wavelengths required. In this case, the K-th multiplexer should be omitted. The rest of the multiplexers (denoted by broken trapezoids) are optional, if a N × N star coupler is used instead of a splitter, as in Fig. 1(b). However, in practice, multiplexers might be required, in order to reduce adjacent channel crosstalk. (b) Layout of a receiver card with K channel selection stages. The numbering of the selection stages is done in reverse order from left to right. The MUX/DMUX pair corresponding to the K-th order channel selector (denoted by broken trapezoids) might be omitted if the K-th multiplexing stage at the transmitter is implemented using spatial division multiplexing (SDM) of nk optical fibers.

Number of SOAs required per receiver card for (a) 256, (b) 72, and (c) 96 channels partitioned in tributaries of Κselection stages. Solid line: Eq. (11). (d) Comparison of the optimality of the best channel selectors for 64, 72, 96 and 256 channels, as a function of the number of selection stages

(a) Example of transmitter/receiver numbering in a 64 × 64 broadcast and select architecture. In parentheses, channel indices are expressed in base-4. In this example, the transmitter with index #37 [(211)4in base-4] is connected to the receiver with index #16. (b) Layout of the 16-th receiver card with 3 channel selection stages. The SOA numbering of each selection stage is shown. The three digits of the base-4 transmitter index are used to set the shaded (red) SOAs ON at the three selection stages.

The SOA setting shown in Fig. 14(b) selects the channel with index #37 out of the 64 wavelength tree, by first selecting the third fiber, then, the second waveband of this fiber, and finally, the second channel in this waveband (thick solid line).